A080400 Largest squarefree number dividing phi(n).

1, 1, 2, 2, 2, 2, 6, 2, 6, 2, 10, 2, 6, 6, 2, 2, 2, 6, 6, 2, 6, 10, 22, 2, 10, 6, 6, 6, 14, 2, 30, 2, 10, 2, 6, 6, 6, 6, 6, 2, 10, 6, 42, 10, 6, 22, 46, 2, 42, 10, 2, 6, 26, 6, 10, 6, 6, 14, 58, 2, 30, 30, 6, 2, 6, 10, 66, 2, 22, 6, 70, 6, 6, 6, 10, 6, 30, 6, 78, 2, 6, 10, 82, 6, 2, 42, 14, 10, 22

Offset

1,3

Comments

Also largest squarefree number dividing Carmichael's lambda, A002322(n). - Antti Karttunen, Jul 17 2017

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Formula

a(n) = A007947(A000010(n)).

a(m * n) = A007947(a(m) * a(n)) if gcd(m, n) = 1. - David A. Corneth, Jul 16 2017

a(n) = A007947(A002322(n)). - Antti Karttunen, Jul 17 2017

Mathematica

Table[Max[Select[Divisors[EulerPhi[n]], SquareFreeQ]], {n, 90}] (* Harvey P. Dale, Jul 05 2012 *)
a[n_] := Times @@ FactorInteger[EulerPhi[n]][[;; , 1]]; Array[a, 100] (* Amiram Eldar, Jun 18 2022 *)

Prog

(PARI) A080400(n) = factorback(factorint(eulerphi(n))[, 1]); \\ Antti Karttunen & David A. Corneth, Jul 16 2017

Crossrefs

Cf. A000010, A002322, A007947, A034380, A289624.

Sequence in context: A163368 A151948 A349923 * A351031 A328236 A119462

Adjacent sequences: A080397 A080398 A080399 * A080401 A080402 A080403

Keyword

nonn

Author

Labos Elemer, Mar 19 2003

Status

approved